David Cameron is facing a revolt in his own Oxfordshire "backyard" as local Tories join a national outcry over council tax reforms that they say will cost people on low earnings more than £420 a year from next April.

Tory-run West Oxfordshire district council, which covers the prime minister's Witney constituency, has decided to go it alone and keep the existing system throughout next year, effectively snubbing Cameron's government.

Plans to scrap council tax benefit and leave it to individual councils to devise their own support schemes from April next year are part of the government's drive to devolve power to the local level, while slashing costs at the same time. In 2010-11 council tax benefit was paid to 5.8 million people at a cost of £4.82bn. At the moment Whitehall covers 100% of each local authority's costs for the benefit. But from next year they will be given 10% less to run their own schemes.

West Oxfordshire and other councils across the country are protesting, however, that after they have met legal obligations to protect pensioners, the disabled and families with children, the 10% cut will mean that people on low earnings will be hit disproportionately. It estimates that working-age people who currently pay nothing will suddenly have to find £420 a year from their other state benefits.

In an internal report, West Oxfordshire officials state: "This approach does not meet the policy intention of incentivising work. Because of the way the benefit would be reduced progressively as incomes rise, councils argue the reform will deter many from seeking work."

The report also suggests that the cost and inconvenience of collecting small sums from people without the means to pay will make the whole system unworkable. The council will therefore defy government and postpone any change until 2014, making up the financial shortfall from other parts of the budget.

Across the country there are similar protests. In June council leaders from 12 councils in Surrey wrote to the chairman of the Local Government Association, Sir Merrick Cockell, voicing their dismay at a policy that was rushed and badly thought through. "We are concerned at the level of impact on working-age claimants with the 10% funding reduction in actual fact translating to more like a 20% or 25% reduction [in relief] being required after allowing for pensioners and other protected groups," they told Cockell.

"We feel a rushed implementation of a new scheme might lead to penalising claimants who already go out to work, which has the opposite effect of what the coalition government wants. This does not seem joined up with the current emphasis on helping 'troubled families'."

Dave Prentis, general secretary of the public sector union Unison, said the changes, if implemented, would be the last straw for 800,000 low-paid workers. "The Tories are shooting themselves in the foot by cutting help for low-paid workers, because it leaves them with even less money and reduces the financial benefits of being in work. This is not just being said by Unison; it is the advice of Conservative council leaders and the local council in David Cameron's own constituency."

The "social injustice" of the policy was all the greater as it would come into effect on the same day as the top rate of tax was cut from 50p to 45p for high earners.

At the end of July, Councillor John Weighell, the leader of North Yorkshire county council, wrote to the communities secretary, Eric Pickles, complaining that the plans would lead to a "postcode lottery", with charges dependent on the local pensioner population. "The lottery element of a council's demographic makeup makes an impossibility of creating a local scheme which is sensitive to the needs of local residents," he wrote.

Hilary Benn, the shadow secretary of state for communities and local government, said: "When even David Cameron's own council says it's unfair to increase council tax on the poorest on the very same day that high earners will get a whopping great reduction in income tax, we know just how out of touch the prime minister has become.

"In the last two years, it is the least well-off councils that have faced the biggest cuts from central government. It will be much harder for these authorities to make up for this additional cut in council tax benefit funding, which is being imposed on their poorest residents by Eric Pickles when times are tough enough as it is."